Answer:
See Below.
Step-by-step explanation:
We are given that:

Where <em>I₀</em> and <em>k</em> are constants.
And we want to prove that:

From the original equation, take the derivative of both sides with respect to <em>t</em>. Hence:
![\displaystyle \frac{d}{dt}\left[I\right] = \frac{d}{dt}\left[I_0e^{-kt}\right]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI%5Cright%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5BI_0e%5E%7B-kt%7D%5Cright%5D)
Differentiate. Since <em>I₀ </em>is a constant:
![\displaystyle \frac{dI}{dt} = I_0\left(\frac{d}{dt}\left[ e^{-kt}\right]\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7BdI%7D%7Bdt%7D%20%3D%20I_0%5Cleft%28%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%5B%20e%5E%7B-kt%7D%5Cright%5D%5Cright%29)
Using the chain rule:

We have:

Substitute:

Distribute and simplify:

Hence proven.
Well 3 divided by 100 is 3 hundredths. 3/100=.03 that would be an example. another is 30000 divided by 100. that would be 300. you just take away 2 zeros for that one.
Answer:
20 friends
Step-by-step explanation:
9 FRIENDS
2 HOURS
10 PEOPLE
2 HOURS
30 PEOPLE
2 HOURS
WORKS :D
Sorry if this is a little weird I did it the way I did it but I know the answer is correct. The work may not seem right to you -.- but :D I understand it...
This is the good part of Trigonometry, actually measuring triangles. It's much better than all the identities around sine and cosine and the rest, which actually have more to do with circles than triangles.
This part of trig has a short menu:
Law of Cosines. Three ways to write it, one is 
Law of Sines: 
Triangle angles: 
and two special cases of the Law of Cosines, the Pythagorean Theorem

and the Collinear Points Theorem:


Here we choose Triangle Angles followed by Law of Sines:
A = 180 - 105 -15 = 60 degrees


Answer: 1.8 cm
When I was a student we'd be expected to get
exactly and get

But that was before online homework.